The guests at this publicised dinner included Steve Barclay MP from the Department for Exiting the EU and Olly Robbins, Mrs May's Europe adviser from Number 10.

With them were Michel Barnier from the European Commission and his two deputies: Sabine Weyand and Stephanie Riso.

The host was the UK's permanent representative to the EU, Sir Tim Barrow.

It was, judging by the menu, a delicious meal. Pan-fried North Sea sole with Scottish scallops and Welsh samphire followed by roast duck breast, then pear parfait and British cheeses. All washed down with Sancerre and St Emilion.

The key focus of the dinner was to explore ways to get the Withdrawal Agreement through Westminster despite the fact that the EU won't reopen it or remove the backstop.

Image:Mr Barnier said a Withdrawal Agreement will not be opened

After a couple of hours, Michel Barnier delivered with a familiar message: "We held constructive talks. It's clear from our side that we are not going to reopen the Withdrawal Agreement but we will continue our discussion in the coming days. That is all."

The feeling among a critical number of MPs in Westminster, as voiced by Boris Johnson this week, is "of course they'll say that now. But soon they'll budge".

A statement from a UK spokesperson said: "The meeting was constructive and Mr Barclay and Mr Barnier agreed to further talks in the coming days and that their teams would continue to work in the meantime on finding a way forward."

But in another dining room in the same building (presumably eating from the same menu) was a much more curious gathering.

Just after 7pm, Sky News cameras spotted the former president of the European Council, Herman Van Rompuy, arriving by limo at the residence.

If you don't remember Mr Van Rompuy, you may remember the extraordinary moment when Nigel Farage called him a "low-grade bank clerk" to his face in the European Parliament chamber in 2011.

"Who are you?!" Mr Farage had jeered. "You have the appearance of a damp rag and the charisma of a low-grade bank clerk."

Image:Sky News was told that Herman Van Rompuy attended a private dinner with David Lidington MP

It was a moment that was as embarrassing to British europhiles as it was thrilling to eurosceptics. Anyway - what was Mr Van Rompuy doing at the British residence in Brussels?

Well I'm told he was attending a separate private dinner with Mrs May's deputy David Lidington MP. And I am told that it was a meeting Mrs May had specifically requested to discuss changes to Irish backstop.

The team at 10 Downing Street see Mr Van Rompuy as an "influencer", and David Lidington was the man to meet him.

Many on this side of the Channel consider Mr Lidington to be one of the few senior British politicians who really understands.

He was David Cameron's Europe minister from 2010 to 2016 and is seen as a very capable politician and diplomat - despite being unsuccessful in Mr Cameron's bid to secure concessions from the EU which would persuade the British public to vote to remain in the EU.

When you mention Mr Lidington's name in Brussels - at the commission, the council or the parliament - people tend to speak highly of him. That's more than can be said for pretty much every other senior UK politician.

Mr Lidington and Mr Van Rompuy also know each other. There is an existing rapport.

A few months ago, Mr Van Rompuy told The Observer that a British threat of no deal would not spook the EU side into moving position.

"Those [no deal] threats will not work vis-a-vis the European Union... I cannot imagine that a British prime minister or a responsible British government is even considering seriously a no deal, playing with the economic future of the country and its people," he said in August last year.

Did he say the same privately at the Monday night dinner? We don't know how the Lidington/Van Rompuy dinner went.

But I am told that after Mr Van Rompuy left the residence, Mr Lidington switched dining rooms to catch the tail end of the other dinner - the one with Steve Barclay and Michel Barnier. They all had coffee together.

Mrs May is urging MPs to give her a little more time to improve the Brexit deal.

She's asking them not to tie her hands by forcing her to extend Article 50, thus delaying Brexit. She is using the clock and threat of "no deal" to her favour for now.

When we look back at this Brexit process we may discover that innocuous private dinners, like Monday night's between Mrs May's deputy and the former European Council Ppresident, were key moments.

Right now the UK needs all the "influencers" it can get. Herman Van Rompuy is one.